"""
Betweenness centrality measures for subsets of nodes.
"""
#    Copyright (C) 2004-2011 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""

__all__ = ['betweenness_centrality_subset',
           'edge_betweenness_centrality_subset',
           'betweenness_centrality_source']

import networkx as nx

from networkx.algorithms.centrality.betweenness import\
    _single_source_dijkstra_path_basic as dijkstra
from networkx.algorithms.centrality.betweenness import\
    _single_source_shortest_path_basic as shortest_path


def betweenness_centrality_subset(G,sources,targets,
                                  normalized=False,
                                  weight=None):
    """Compute betweenness centrality for a subset of nodes.

    .. math::

       c_B(v) =\sum_{s\in S, t \in T} \frac{\sigma(s, t|v)}{\sigma(s, t)}

    where `S` is the set of sources, `T` is the set of targets,
    `\sigma(s, t)` is the number of shortest `(s, t)`-paths, 
    and `\sigma(s, t|v)` is the number of those paths
    passing through some  node `v` other than `s, t`. 
    If `s = t`, `\sigma(s, t) = 1`,
    and if `v \in {s, t}`,  `\sigma(s, t|v) = 0` [2]_.


    Parameters
    ----------
    G : graph

    sources: list of nodes
      Nodes to use as sources for shortest paths in betweenness

    targets: list of nodes
      Nodes to use as targets for shortest paths in betweenness

    normalized : bool, optional
      If True the betweenness values are normalized by `2/((n-1)(n-2))` 
      for graphs, and `1/((n-1)(n-2))` for directed graphs where `n` 
      is the number of nodes in G.
       
    weight : None or string, optional  
      If None, all edge weights are considered equal.
      Otherwise holds the name of the edge attribute used as weight.

    Returns
    -------
    nodes : dictionary
       Dictionary of nodes with betweenness centrality as the value.

    See Also
    --------
    edge_betweenness_centrality
    load_centrality

    Notes
    -----
    The basic algorithm is from [1]_.

    For weighted graphs the edge weights must be greater than zero.
    Zero edge weights can produce an infinite number of equal length 
    paths between pairs of nodes.

    The normalization might seem a little strange but it is the same
    as in betweenness_centrality() and is designed to make
    betweenness_centrality(G) be the same as
    betweenness_centrality_subset(G,sources=G.nodes(),targets=G.nodes()).

    
    References
    ----------
    .. [1] Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
       Journal of Mathematical Sociology 25(2):163-177, 2001.
       http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness 
       Centrality and their Generic Computation. 
       Social Networks 30(2):136-145, 2008.
       http://www.inf.uni-konstanz.de/algo/publications/b-vspbc-08.pdf
    """
    b=dict.fromkeys(G,0.0) # b[v]=0 for v in G
    for s in sources:
        # single source shortest paths
        if weight is None:  # use BFS
            S,P,sigma=shortest_path(G,s)
        else:  # use Dijkstra's algorithm
            S,P,sigma=dijkstra(G,s,weight)
        b=_accumulate_subset(b,S,P,sigma,s,targets)
    b=_rescale(b,len(G),normalized=normalized,directed=G.is_directed())
    return b


def edge_betweenness_centrality_subset(G,sources,targets,
                                       normalized=False,
                                       weight=None):
    """Compute betweenness centrality for edges for a subset of nodes.

    .. math::

       c_B(v) =\sum_{s\in S,t \in T} \frac{\sigma(s, t|e)}{\sigma(s, t)}

    where `S` is the set of sources, `T` is the set of targets,
    `\sigma(s, t)` is the number of shortest `(s, t)`-paths, 
    and `\sigma(s, t|e)` is the number of those paths
    passing through edge `e` [2]_.

    Parameters
    ----------
    G : graph
      A networkx graph 

    sources: list of nodes
      Nodes to use as sources for shortest paths in betweenness

    targets: list of nodes
      Nodes to use as targets for shortest paths in betweenness

    normalized : bool, optional
      If True the betweenness values are normalized by `2/(n(n-1))` 
      for graphs, and `1/(n(n-1))` for directed graphs where `n` 
      is the number of nodes in G.
       
    weight : None or string, optional  
      If None, all edge weights are considered equal.
      Otherwise holds the name of the edge attribute used as weight.

    Returns
    -------
    edges : dictionary
       Dictionary of edges with Betweenness centrality as the value.
        
    See Also
    --------
    betweenness_centrality
    edge_load

    Notes
    -----
    The basic algorithm is from [1]_.

    For weighted graphs the edge weights must be greater than zero.
    Zero edge weights can produce an infinite number of equal length 
    paths between pairs of nodes.

    The normalization might seem a little strange but it is the same
    as in edge_betweenness_centrality() and is designed to make
    edge_betweenness_centrality(G) be the same as
    edge_betweenness_centrality_subset(G,sources=G.nodes(),targets=G.nodes()).

    References
    ----------
    .. [1] Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
       Journal of Mathematical Sociology 25(2):163-177, 2001.
       http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness 
       Centrality and their Generic Computation. 
       Social Networks 30(2):136-145, 2008.
       http://www.inf.uni-konstanz.de/algo/publications/b-vspbc-08.pdf

    """

    b=dict.fromkeys(G,0.0) # b[v]=0 for v in G
    b.update(dict.fromkeys(G.edges(),0.0)) # b[e] for e in G.edges()
    for s in sources:
        # single source shortest paths
        if weight is None:  # use BFS
            S,P,sigma=shortest_path(G,s)
        else:  # use Dijkstra's algorithm
            S,P,sigma=dijkstra(G,s,weight)
        b=_accumulate_edges_subset(b,S,P,sigma,s,targets)
    for n in G: # remove nodes to only return edges 
        del b[n]
    b=_rescale_e(b,len(G),normalized=normalized,directed=G.is_directed())
    return b

# obsolete name
def betweenness_centrality_source(G,normalized=True,weight=None,sources=None):
    if sources is None:
        sources=G.nodes()
    targets=G.nodes()
    return betweenness_centrality_subset(G,sources,targets,normalized,weight)


def _accumulate_subset(betweenness,S,P,sigma,s,targets):
    delta=dict.fromkeys(S,0)
    target_set=set(targets)
    while S:
        w=S.pop()
        for v in P[w]:
            if w in target_set:
                delta[v]+=(sigma[v]/sigma[w])*(1.0+delta[w])
            else:
                delta[v]+=delta[w]/len(P[w])
        if w != s:
            betweenness[w]+=delta[w]
    return betweenness

def _accumulate_edges_subset(betweenness,S,P,sigma,s,targets):
    delta=dict.fromkeys(S,0)
    target_set=set(targets)
    while S:
        w=S.pop()
        for v in P[w]:
            if w in target_set:
                c=(sigma[v]/sigma[w])*(1.0+delta[w])
            else:
                c=delta[w]/len(P[w])
            if (v,w) not in betweenness:
                betweenness[(w,v)]+=c
            else:
                betweenness[(v,w)]+=c
            delta[v]+=c
        if w != s:
            betweenness[w]+=delta[w]
    return betweenness




def _rescale(betweenness,n,normalized,directed=False):
    if normalized is True:
        if n <=2:
            scale=None  # no normalization b=0 for all nodes
        else:
            scale=1.0/((n-1)*(n-2))
    else: # rescale by 2 for undirected graphs
        if not directed:
            scale=1.0/2.0
        else:
            scale=None
    if scale is not None:
        for v in betweenness:
            betweenness[v] *= scale
    return betweenness

def _rescale_e(betweenness,n,normalized,directed=False):
    if normalized is True:
        if n <=1:
            scale=None  # no normalization b=0 for all nodes
        else:
            scale=1.0/(n*(n-1))
    else: # rescale by 2 for undirected graphs
        if not directed:
            scale=1.0/2.0
        else:
            scale=None
    if scale is not None:
        for v in betweenness:
            betweenness[v] *= scale
    return betweenness
